A process for treating a semiconductor wafer such as a silicon wafer includes controlling the in-plane temperature distribution of the silicon wafer as desired while controlling the temperature of the silicon wafer to a temperature setpoint.
For instance, according to a known method, heaters are each incorporated in an independent control loop so that the semiconductor wafer is simultaneously heated using a plurality of temperature adjusters.
Regarding the above temperature control for a semiconductor wafer, it is necessary that control variables should have a constant deviation from a reference control variable until the temperature reaches a setpoint and that the temperature should be maintained at the setpoint irrespective of any disturbance. In connection with the above, a master-slave control method and a gradient temperature control method are typically known (see, for instance, Patent Literature 1: JP-A-7-200076 and Patent Literature 2: JP-A-2000-187514).
In the master-slave control method, one of a plurality of control loops is controlled as a master, and a deviation between a control variable (a setpoint) of the master loop and a control variable of a slave loop(s) is calculated and controlled so that the slave loop(s) follows the behavior of the master loop.
In the gradient temperature control method, an average of control variables for loops is defined as a representative variable, and a difference between the control variables for the loops is defined as a gradient variable (another control variable), the representative variable following a setpoint with the gradient variable being kept constant. The control variables are transformed using a transformation matrix. Further, a non-interfering matrix is used to reduce interference among the loops, and a manipulated variable transformation matrix is used to return the control variables to the original dimension.
However, the techniques disclosed in Patent Literatures 1 and 2 have a problem of lowering a control performance because when the temperature adjusters (an actuator) undergo saturation in the process of responding to the setpoint, further compensation is unavailable.